# A Proof “P≠NP” for P vs. NP Problem by Multiple-Tape Turing-Machine

*Yaozhi Jiang*

*Journal of Mathematics Research*, 2020, vol. 12, issue 4, 1

**Abstract:**
P vs. NP problem is very important research direction in computation complexity theory. In this paper author, by an engineer’s viewpoint, establishes universal multiple-tape Turing-machine and k-homogeneous multiple-tape Turing-machine, and by them we can obtain an unified mathematical model for algorithm-tree, from the unified model for algorithm-tree, we can conclude that computation complexity for serial processing NP problem if under parallel processing sometimes we can obtain P=NP in time-complexity, but that will imply another NP, non-deterministic space-complexity NP, i.e., under serial processing P≠NP in space-complexity, and the result is excluded the case of NP problem that there exists a faster algorithm to replace the brute-force algorithm, and hence we can proof that under parallel processing time-complexity is depended on space-complexity, and vice verse, within P vs. NP problem, this point is just the natural property of P vs. NP problem so that “P≠NP ”.

**JEL-codes:** R00 Z0 (search for similar items in EconPapers)

**Date:** 2020

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